Pluck a string and only certain notes survive. A string fixed at both ends resonates only at its harmonics — each with fixed nodes and swinging antinodes.
Standing Waves on a StringLive
harmonics · nodes & antinodes
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A string fixed at both ends can only vibrate at its harmonics. Each mode n has n+1 nodes (pink) that stay still while the antinodes swing — the physics of every stringed instrument.
Reading this result: 3 half-wavelengths fit the string, so there are 3 antinodes (max swing) and 4 nodes (fixed points). At harmonic n = 3 the string sings at 330 Hz — exactly 3× the 110 Hz fundamental, and the wavelength is 2L/3.
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How it works
A string clamped at both ends supports standing waves whose wavelengths fit an exact number of half-wavelengths. Each harmonic n has n antinodes and n+1 nodes. This is the physics of guitars, violins, and organ pipes — and of resonance everywhere.
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